A shopkeeper marked the price 20% more than its cost price. If he allows a discount of 30%, then find his loss percent.

Correct — C. Take CP = ₹100, because every number in the question is a percentage and the answer is one too.

Marked price = 100 + 20% of 100 = ₹120
Discount = 30% of 120 = ₹36
Selling price = 120 − 36 = ₹84

Loss = 100 − 84 = ₹16
Loss% = (16 ⁄ 100) × 100 = 16% → option (c)

Why the others are wrong

• (a)
  20% — 20% is the mark-up the question gives, not the loss. The discount is taken on ₹120 and the loss is measured on ₹100, so the two percentages sit on different bases and cannot cancel.
• (b)
  15% — 1.20 × 0.70 = 0.84, so SP is 84% of CP and the loss is pinned at 16%. A 15% loss would need a discount of about 29.2% on the same 20% mark-up.
• (d)
  25% — A 25% loss means SP = 0.75 × CP, which would need a discount of 37.5% on a 20% mark-up, not 30%. The discount and the loss are not the same quantity read twice.

Three prices, two multipliers. The mark-up acts on the cost price to make the marked price, and the discount acts on the marked price to make the selling price:
MP = CP × (1 + mark-up), SP = MP × (1 − discount).

Put them together and the whole question is one product: SP = CP × 1.20 × 0.70 = 0.84 CP. Anything below 1 is a loss, anything above it a gain.

Profit and loss per cent are always measured against the cost price. That is why 30% − 20% is meaningless here: the 30% is a slice of 120, the answer a slice of 100.

Key facts

• MP = CP × (1 + mark-up) and SP = MP × (1 − discount).
• Combining them, SP = CP × (1 + mark-up) × (1 − discount), which here is 1.20 × 0.70 = 0.84.
• Profit or loss per cent is computed on the cost price, never on the marked price.

Common traps

• Taking the 30% discount on the cost price instead of the marked price
• Subtracting 30% − 20% and answering 10%
• Computing the loss against the marked price, which gives 30% instead of 16%

No directly related past PYQ was found.